%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SWV372+1 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 22:56:03 EDT 2023 % Result : Theorem 23.95s 3.90s % Output : Proof 23.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SWV372+1 : TPTP v8.1.2. Released v3.3.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n013.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Tue Aug 29 02:49:47 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.60 Running up to 7 provers in parallel. % 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 4.01/1.22 Prover 4: Preprocessing ... % 4.01/1.22 Prover 1: Preprocessing ... % 4.01/1.26 Prover 6: Preprocessing ... % 4.01/1.26 Prover 2: Preprocessing ... % 4.01/1.26 Prover 5: Preprocessing ... % 4.01/1.26 Prover 0: Preprocessing ... % 4.01/1.26 Prover 3: Preprocessing ... % 9.16/2.01 Prover 1: Warning: ignoring some quantifiers % 10.71/2.14 Prover 1: Constructing countermodel ... % 10.82/2.16 Prover 3: Warning: ignoring some quantifiers % 10.82/2.16 Prover 6: Proving ... % 10.82/2.16 Prover 5: Proving ... % 10.82/2.20 Prover 3: Constructing countermodel ... % 11.21/2.22 Prover 4: Constructing countermodel ... % 11.57/2.26 Prover 2: Proving ... % 11.57/2.27 Prover 0: Proving ... % 16.83/2.98 Prover 1: gave up % 16.83/2.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 16.83/3.04 Prover 7: Preprocessing ... % 18.82/3.27 Prover 7: Warning: ignoring some quantifiers % 18.82/3.31 Prover 7: Constructing countermodel ... % 20.48/3.50 Prover 3: gave up % 20.48/3.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 21.25/3.57 Prover 8: Preprocessing ... % 23.58/3.86 Prover 7: Found proof (size 102) % 23.58/3.86 Prover 7: proved (875ms) % 23.58/3.87 Prover 0: stopped % 23.58/3.87 Prover 2: stopped % 23.58/3.87 Prover 5: stopped % 23.58/3.87 Prover 6: stopped % 23.58/3.87 Prover 4: stopped % 23.58/3.88 Prover 8: Warning: ignoring some quantifiers % 23.95/3.89 Prover 8: Constructing countermodel ... % 23.95/3.90 Prover 8: stopped % 23.95/3.90 % 23.95/3.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.95/3.90 % 23.95/3.91 % SZS output start Proof for theBenchmark % 23.95/3.92 Assumptions after simplification: % 23.95/3.92 --------------------------------- % 23.95/3.92 % 23.95/3.92 (ax36) % 23.95/3.94 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, % 23.95/3.94 create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | check_cpq(v2)) % 23.95/3.94 % 23.95/3.94 (ax39) % 23.95/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ % 23.95/3.94 (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 23.95/3.94 ~ contains_cpq(v4, v3) | contains_slb(v1, v3)) & ! [v0: $i] : ! [v1: $i] : % 23.95/3.94 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (triple(v0, v1, v2) = v4) | ~ % 23.95/3.94 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ contains_slb(v1, v3) | % 23.95/3.94 contains_cpq(v4, v3)) % 23.95/3.94 % 23.95/3.94 (ax40) % 23.95/3.94 $i(bad) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 23.95/3.94 v2) | ~ $i(v1) | ~ $i(v0) | ~ ok(v2)) % 23.95/3.94 % 23.95/3.94 (ax46) % 23.95/3.94 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.95/3.94 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 23.95/3.94 (triple(v0, create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3))) % 23.95/3.94 % 23.95/3.94 (ax47) % 23.95/3.94 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.95/3.94 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.95/3.94 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 23.95/3.94 : ? [v6: $i] : ? [v7: $i] : (findmin_pqp_res(v0) = v5 & $i(v5) & % 23.95/3.94 (contains_slb(v1, v5) | (v7 = v4 & triple(v0, v6, bad) = v4 & % 23.95/3.94 update_slb(v1, v5) = v6 & $i(v6) & $i(v4))))) % 23.95/3.94 % 23.95/3.94 (ax48) % 23.95/3.95 $i(bad) & $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.95/3.95 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.95/3.95 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 23.95/3.95 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 & % 23.95/3.95 $i(v5) & ( ~ contains_slb(v1, v5) | (v8 = v4 & triple(v0, v7, bad) = v4 & % 23.95/3.95 update_slb(v1, v5) = v7 & $i(v7) & $i(v4)) | (lookup_slb(v1, v5) = v6 % 23.95/3.95 & $i(v6) & ~ strictly_less_than(v5, v6))))) % 23.95/3.95 % 23.95/3.95 (ax49) % 23.95/3.95 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 23.95/3.95 [v4: $i] : ! [v5: $i] : (v1 = create_slb | ~ (findmin_pqp_res(v0) = v3) | ~ % 23.95/3.95 (triple(v0, v4, v2) = v5) | ~ (update_slb(v1, v3) = v4) | ~ $i(v2) | ~ % 23.95/3.95 $i(v1) | ~ $i(v0) | ~ contains_slb(v1, v3) | ? [v6: $i] : ? [v7: $i] : % 23.95/3.95 ? [v8: $i] : ((v8 = v5 & triple(v0, v1, v2) = v7 & findmin_cpq_eff(v7) = v5 % 23.95/3.95 & $i(v7) & $i(v5)) | (lookup_slb(v1, v3) = v6 & $i(v6) & ~ % 23.95/3.95 less_than(v6, v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.95/3.95 $i] : ! [v4: $i] : (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.95/3.95 (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] % 23.95/3.95 : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : (findmin_pqp_res(v0) = v5 & % 23.95/3.95 $i(v5) & ( ~ contains_slb(v1, v5) | (v8 = v4 & triple(v0, v7, v2) = v4 & % 23.95/3.95 update_slb(v1, v5) = v7 & $i(v7) & $i(v4)) | (lookup_slb(v1, v5) = v6 % 23.95/3.95 & $i(v6) & ~ less_than(v6, v5))))) % 23.95/3.95 % 23.95/3.95 (ax51) % 23.95/3.95 $i(create_slb) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 23.95/3.95 [v4: $i] : (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, % 23.95/3.95 v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (findmin_pqp_res(v0) % 23.95/3.95 = v4 & $i(v4))) % 23.95/3.95 % 23.95/3.95 (ax52) % 23.95/3.95 ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) | ? % 23.95/3.95 [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & findmin_cpq_eff(v0) = % 23.95/3.95 v3 & remove_cpq(v3, v1) = v2 & $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: % 23.95/3.95 $i] : ( ~ (removemin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 23.95/3.95 $i] : (findmin_cpq_res(v0) = v3 & findmin_cpq_eff(v0) = v2 & % 23.95/3.95 remove_cpq(v2, v3) = v1 & $i(v3) & $i(v2) & $i(v1))) & ! [v0: $i] : ! % 23.95/3.95 [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: % 23.95/3.95 $i] : (findmin_cpq_res(v0) = v3 & removemin_cpq_eff(v0) = v2 & % 23.95/3.95 remove_cpq(v1, v3) = v2 & $i(v3) & $i(v2))) % 23.95/3.95 % 23.95/3.95 (ax54) % 23.95/3.95 $i(create_slb) & $i(create_pq) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.95/3.95 (triple(v0, create_slb, v1) = v2) | ~ $i(v1) | ~ $i(v0) | i(v2) = % 23.95/3.95 create_pq) % 23.95/3.95 % 23.95/3.95 (l8_co) % 23.95/3.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 23.95/3.95 $i] : ? [v6: $i] : (i(v3) = v5 & findmin_cpq_res(v3) = v6 & triple(v0, v1, % 23.95/3.95 v2) = v3 & findmin_cpq_eff(v3) = v4 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 23.95/3.95 $i(v2) & $i(v1) & $i(v0) & phi(v4) & ~ contains_pq(v5, v6)) % 23.95/3.95 % 23.95/3.95 (l8_l9) % 23.95/3.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, % 23.95/3.95 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: % 23.95/3.95 $i] : ((findmin_cpq_res(v3) = v4 & $i(v4) & contains_cpq(v3, v4)) | % 23.95/3.96 (findmin_cpq_eff(v3) = v5 & $i(v5) & ~ ok(v5)))) % 23.95/3.96 % 23.95/3.96 (l8_lX) % 23.95/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (triple(v0, v1, % 23.95/3.96 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ phi(v3) | ok(v3)) % 23.95/3.96 % 23.95/3.96 (l8_li56) % 23.95/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 23.95/3.96 $i] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ % 23.95/3.96 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ contains_cpq(v4, v3) | contains_pq(v5, % 23.95/3.96 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 23.95/3.96 : ! [v5: $i] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ $i(v3) | % 23.95/3.96 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ contains_pq(v5, v3) | contains_cpq(v4, % 23.95/3.96 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] % 23.95/3.96 : ( ~ (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.95/3.96 $i(v0) | ~ contains_cpq(v4, v3) | ? [v5: $i] : (i(v4) = v5 & $i(v5) & % 23.95/3.96 contains_pq(v5, v3))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.95/3.96 $i] : ! [v4: $i] : ( ~ (triple(v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | % 23.95/3.96 ~ $i(v1) | ~ $i(v0) | contains_cpq(v4, v0) | ? [v5: $i] : (i(v4) = v5 & % 23.95/3.96 $i(v5) & ~ contains_pq(v5, v0))) % 23.95/3.96 % 23.95/3.96 (function-axioms) % 23.95/3.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 % 23.95/3.96 | ~ (triple(v4, v3, v2) = v1) | ~ (triple(v4, v3, v2) = v0)) & ! [v0: $i] % 23.95/3.96 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (remove_pqp(v3, v2) % 23.95/3.96 = v1) | ~ (remove_pqp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.95/3.96 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_pqp(v3, v2) = v1) | ~ % 23.95/3.96 (insert_pqp(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 23.95/3.96 [v3: $i] : (v1 = v0 | ~ (remove_cpq(v3, v2) = v1) | ~ (remove_cpq(v3, v2) = % 23.95/3.96 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.95/3.96 ~ (insert_cpq(v3, v2) = v1) | ~ (insert_cpq(v3, v2) = v0)) & ! [v0: $i] : % 23.95/3.96 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (update_slb(v3, v2) = % 23.95/3.96 v1) | ~ (update_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.95/3.96 $i] : ! [v3: $i] : (v1 = v0 | ~ (lookup_slb(v3, v2) = v1) | ~ % 23.95/3.96 (lookup_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 23.95/3.96 [v3: $i] : (v1 = v0 | ~ (remove_slb(v3, v2) = v1) | ~ (remove_slb(v3, v2) = % 23.95/3.96 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.95/3.96 ~ (pair(v3, v2) = v1) | ~ (pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 23.95/3.96 : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (insert_slb(v3, v2) = v1) | ~ % 23.95/3.96 (insert_slb(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 23.95/3.96 [v3: $i] : (v1 = v0 | ~ (removemin_pq_res(v3, v2) = v1) | ~ % 23.95/3.96 (removemin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.95/3.96 ! [v3: $i] : (v1 = v0 | ~ (removemin_pq_eff(v3, v2) = v1) | ~ % 23.95/3.96 (removemin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.95/3.96 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_res(v3, v2) = v1) | ~ % 23.95/3.96 (findmin_pq_res(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.95/3.96 ! [v3: $i] : (v1 = v0 | ~ (findmin_pq_eff(v3, v2) = v1) | ~ % 23.95/3.96 (findmin_pq_eff(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.95/3.96 ! [v3: $i] : (v1 = v0 | ~ (remove_pq(v3, v2) = v1) | ~ (remove_pq(v3, v2) = % 23.95/3.96 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 23.95/3.96 ~ (insert_pq(v3, v2) = v1) | ~ (insert_pq(v3, v2) = v0)) & ! [v0: $i] : ! % 23.95/3.96 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (i(v2) = v1) | ~ (i(v2) = v0)) & ! % 23.95/3.96 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_res(v2) = % 23.95/3.96 v1) | ~ (removemin_cpq_res(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.95/3.96 [v2: $i] : (v1 = v0 | ~ (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) % 23.95/3.96 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.95/3.96 (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) & ! [v0: $i] : % 23.95/3.96 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (removemin_cpq_eff(v2) = v1) | ~ % 23.95/3.96 (removemin_cpq_eff(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.95/3.96 (v1 = v0 | ~ (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 23.95/3.96 % 23.95/3.96 Further assumptions not needed in the proof: % 23.95/3.96 -------------------------------------------- % 23.95/3.96 ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax20, ax21, ax22, % 23.95/3.96 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax30, ax31, ax32, ax33, ax34, ax35, % 23.95/3.96 ax37, ax38, ax41, ax42, ax43, ax44, ax45, ax50, ax53, ax55, ax56, ax57, ax58, % 23.95/3.96 ax59, ax6, ax60, ax61, ax62, ax7, ax8, ax9, bottom_smallest, reflexivity, % 23.95/3.96 stricly_smaller_definition, totality, transitivity % 23.95/3.96 % 23.95/3.96 Those formulas are unsatisfiable: % 23.95/3.96 --------------------------------- % 23.95/3.96 % 23.95/3.96 Begin of proof % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax36) implies: % 23.95/3.97 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb, % 23.95/3.97 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | check_cpq(v2)) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax39) implies: % 23.95/3.97 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( % 23.95/3.97 | ~ (triple(v0, v1, v2) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.95/3.97 | $i(v0) | ~ contains_slb(v1, v3) | contains_cpq(v4, v3)) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax40) implies: % 23.95/3.97 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, v1, bad) = % 23.95/3.97 | v2) | ~ $i(v1) | ~ $i(v0) | ~ ok(v2)) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax46) implies: % 23.95/3.97 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (triple(v0, create_slb, % 23.95/3.97 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (triple(v0, % 23.95/3.97 | create_slb, bad) = v3 & findmin_cpq_eff(v2) = v3 & $i(v3))) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax47) implies: % 23.95/3.97 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.95/3.97 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.95/3.97 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.95/3.97 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : (findmin_pqp_res(v0) = v5 & % 23.95/3.97 | $i(v5) & (contains_slb(v1, v5) | (v7 = v4 & triple(v0, v6, bad) = % 23.95/3.97 | v4 & update_slb(v1, v5) = v6 & $i(v6) & $i(v4))))) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax48) implies: % 23.95/3.97 | (6) $i(bad) % 23.95/3.97 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.95/3.97 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.95/3.97 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.95/3.97 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 23.95/3.97 | (findmin_pqp_res(v0) = v5 & $i(v5) & ( ~ contains_slb(v1, v5) | (v8 = % 23.95/3.97 | v4 & triple(v0, v7, bad) = v4 & update_slb(v1, v5) = v7 & % 23.95/3.97 | $i(v7) & $i(v4)) | (lookup_slb(v1, v5) = v6 & $i(v6) & ~ % 23.95/3.97 | strictly_less_than(v5, v6))))) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax49) implies: % 23.95/3.97 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.95/3.97 | (v1 = create_slb | ~ (triple(v0, v1, v2) = v3) | ~ % 23.95/3.97 | (findmin_cpq_eff(v3) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 23.95/3.97 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : % 23.95/3.97 | (findmin_pqp_res(v0) = v5 & $i(v5) & ( ~ contains_slb(v1, v5) | (v8 = % 23.95/3.97 | v4 & triple(v0, v7, v2) = v4 & update_slb(v1, v5) = v7 & $i(v7) % 23.95/3.97 | & $i(v4)) | (lookup_slb(v1, v5) = v6 & $i(v6) & ~ % 23.95/3.97 | less_than(v6, v5))))) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax51) implies: % 23.95/3.97 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.95/3.97 | (v1 = create_slb | ~ (findmin_cpq_res(v3) = v4) | ~ (triple(v0, v1, % 23.95/3.97 | v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 23.95/3.97 | (findmin_pqp_res(v0) = v4 & $i(v4))) % 23.95/3.97 | % 23.95/3.97 | ALPHA: (ax52) implies: % 23.95/3.98 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_eff(v0) = v1) | ~ $i(v0) % 23.95/3.98 | | ? [v2: $i] : ? [v3: $i] : (findmin_cpq_res(v0) = v3 & % 23.95/3.98 | removemin_cpq_eff(v0) = v2 & remove_cpq(v1, v3) = v2 & $i(v3) & % 23.95/3.98 | $i(v2))) % 23.95/3.98 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (findmin_cpq_res(v0) = v1) | ~ $i(v0) % 23.95/3.98 | | ? [v2: $i] : ? [v3: $i] : (removemin_cpq_eff(v0) = v2 & % 23.95/3.98 | findmin_cpq_eff(v0) = v3 & remove_cpq(v3, v1) = v2 & $i(v3) & % 23.95/3.98 | $i(v2))) % 23.95/3.98 | % 23.95/3.98 | ALPHA: (ax54) implies: % 23.95/3.98 | (12) $i(create_slb) % 23.95/3.98 | % 23.95/3.98 | ALPHA: (l8_li56) implies: % 23.95/3.98 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 23.95/3.98 | ! [v5: $i] : ( ~ (i(v4) = v5) | ~ (triple(v0, v1, v2) = v4) | ~ % 23.95/3.98 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ contains_cpq(v4, v3) % 23.95/3.98 | | contains_pq(v5, v3)) % 23.95/3.98 | % 23.95/3.98 | ALPHA: (function-axioms) implies: % 23.95/3.98 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.95/3.98 | (findmin_cpq_eff(v2) = v1) | ~ (findmin_cpq_eff(v2) = v0)) % 23.95/3.98 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.95/3.98 | (findmin_pqp_res(v2) = v1) | ~ (findmin_pqp_res(v2) = v0)) % 23.95/3.98 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.95/3.98 | (findmin_cpq_res(v2) = v1) | ~ (findmin_cpq_res(v2) = v0)) % 23.95/3.98 | % 23.95/3.98 | DELTA: instantiating (l8_co) with fresh symbols all_70_0, all_70_1, all_70_2, % 23.95/3.98 | all_70_3, all_70_4, all_70_5, all_70_6 gives: % 23.95/3.98 | (17) i(all_70_3) = all_70_1 & findmin_cpq_res(all_70_3) = all_70_0 & % 23.95/3.98 | triple(all_70_6, all_70_5, all_70_4) = all_70_3 & % 23.95/3.98 | findmin_cpq_eff(all_70_3) = all_70_2 & $i(all_70_0) & $i(all_70_1) & % 23.95/3.98 | $i(all_70_2) & $i(all_70_3) & $i(all_70_4) & $i(all_70_5) & % 23.95/3.98 | $i(all_70_6) & phi(all_70_2) & ~ contains_pq(all_70_1, all_70_0) % 23.95/3.98 | % 23.95/3.98 | ALPHA: (17) implies: % 23.95/3.98 | (18) ~ contains_pq(all_70_1, all_70_0) % 23.95/3.98 | (19) phi(all_70_2) % 23.95/3.98 | (20) $i(all_70_6) % 23.95/3.98 | (21) $i(all_70_5) % 23.95/3.98 | (22) $i(all_70_4) % 23.95/3.98 | (23) $i(all_70_3) % 23.95/3.98 | (24) findmin_cpq_eff(all_70_3) = all_70_2 % 23.95/3.98 | (25) triple(all_70_6, all_70_5, all_70_4) = all_70_3 % 23.95/3.98 | (26) findmin_cpq_res(all_70_3) = all_70_0 % 23.95/3.98 | (27) i(all_70_3) = all_70_1 % 23.95/3.98 | % 23.95/3.98 | GROUND_INST: instantiating (10) with all_70_3, all_70_2, simplifying with % 23.95/3.98 | (23), (24) gives: % 23.95/3.98 | (28) ? [v0: $i] : ? [v1: $i] : (findmin_cpq_res(all_70_3) = v1 & % 23.95/3.98 | removemin_cpq_eff(all_70_3) = v0 & remove_cpq(all_70_2, v1) = v0 & % 23.95/3.98 | $i(v1) & $i(v0)) % 23.95/3.98 | % 23.95/3.98 | GROUND_INST: instantiating (8) with all_70_6, all_70_5, all_70_4, all_70_3, % 23.95/3.98 | all_70_2, simplifying with (20), (21), (22), (24), (25) gives: % 23.95/3.98 | (29) all_70_5 = create_slb | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 23.95/3.98 | [v3: int] : (findmin_pqp_res(all_70_6) = v0 & $i(v0) & ( ~ % 23.95/3.98 | contains_slb(all_70_5, v0) | (v3 = all_70_2 & triple(all_70_6, v2, % 23.95/3.98 | all_70_4) = all_70_2 & update_slb(all_70_5, v0) = v2 & $i(v2) % 23.95/3.98 | & $i(all_70_2)) | (lookup_slb(all_70_5, v0) = v1 & $i(v1) & ~ % 23.95/3.98 | less_than(v1, v0)))) % 23.95/3.98 | % 23.95/3.98 | GROUND_INST: instantiating (7) with all_70_6, all_70_5, all_70_4, all_70_3, % 23.95/3.98 | all_70_2, simplifying with (20), (21), (22), (24), (25) gives: % 23.95/3.99 | (30) all_70_5 = create_slb | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? % 23.95/3.99 | [v3: int] : (findmin_pqp_res(all_70_6) = v0 & $i(v0) & ( ~ % 23.95/3.99 | contains_slb(all_70_5, v0) | (v3 = all_70_2 & triple(all_70_6, v2, % 23.95/3.99 | bad) = all_70_2 & update_slb(all_70_5, v0) = v2 & $i(v2) & % 23.95/3.99 | $i(all_70_2)) | (lookup_slb(all_70_5, v0) = v1 & $i(v1) & ~ % 23.95/3.99 | strictly_less_than(v0, v1)))) % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (5) with all_70_6, all_70_5, all_70_4, all_70_3, % 23.95/3.99 | all_70_2, simplifying with (20), (21), (22), (24), (25) gives: % 23.95/3.99 | (31) all_70_5 = create_slb | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 23.95/3.99 | (findmin_pqp_res(all_70_6) = v0 & $i(v0) & (contains_slb(all_70_5, v0) % 23.95/3.99 | | (v2 = all_70_2 & triple(all_70_6, v1, bad) = all_70_2 & % 23.95/3.99 | update_slb(all_70_5, v0) = v1 & $i(v1) & $i(all_70_2)))) % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (1) with all_70_6, all_70_4, all_70_3, simplifying % 23.95/3.99 | with (20), (22) gives: % 23.95/3.99 | (32) ~ (triple(all_70_6, create_slb, all_70_4) = all_70_3) | % 23.95/3.99 | check_cpq(all_70_3) % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (4) with all_70_6, all_70_4, all_70_3, simplifying % 23.95/3.99 | with (20), (22) gives: % 23.95/3.99 | (33) ~ (triple(all_70_6, create_slb, all_70_4) = all_70_3) | ? [v0: $i] : % 23.95/3.99 | (triple(all_70_6, create_slb, bad) = v0 & findmin_cpq_eff(all_70_3) = % 23.95/3.99 | v0 & $i(v0)) % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (l8_l9) with all_70_6, all_70_5, all_70_4, % 23.95/3.99 | all_70_3, simplifying with (20), (21), (22), (25) gives: % 23.95/3.99 | (34) ? [v0: $i] : ? [v1: $i] : ((findmin_cpq_res(all_70_3) = v0 & $i(v0) % 23.95/3.99 | & contains_cpq(all_70_3, v0)) | (findmin_cpq_eff(all_70_3) = v1 & % 23.95/3.99 | $i(v1) & ~ ok(v1))) % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (9) with all_70_6, all_70_5, all_70_4, all_70_3, % 23.95/3.99 | all_70_0, simplifying with (20), (21), (22), (25), (26) gives: % 23.95/3.99 | (35) all_70_5 = create_slb | (findmin_pqp_res(all_70_6) = all_70_0 & % 23.95/3.99 | $i(all_70_0)) % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (11) with all_70_3, all_70_0, simplifying with % 23.95/3.99 | (23), (26) gives: % 23.95/3.99 | (36) ? [v0: $i] : ? [v1: $i] : (removemin_cpq_eff(all_70_3) = v0 & % 23.95/3.99 | findmin_cpq_eff(all_70_3) = v1 & remove_cpq(v1, all_70_0) = v0 & % 23.95/3.99 | $i(v1) & $i(v0)) % 23.95/3.99 | % 23.95/3.99 | DELTA: instantiating (28) with fresh symbols all_80_0, all_80_1 gives: % 23.95/3.99 | (37) findmin_cpq_res(all_70_3) = all_80_0 & removemin_cpq_eff(all_70_3) = % 23.95/3.99 | all_80_1 & remove_cpq(all_70_2, all_80_0) = all_80_1 & $i(all_80_0) & % 23.95/3.99 | $i(all_80_1) % 23.95/3.99 | % 23.95/3.99 | ALPHA: (37) implies: % 23.95/3.99 | (38) findmin_cpq_res(all_70_3) = all_80_0 % 23.95/3.99 | % 23.95/3.99 | DELTA: instantiating (36) with fresh symbols all_82_0, all_82_1 gives: % 23.95/3.99 | (39) removemin_cpq_eff(all_70_3) = all_82_1 & findmin_cpq_eff(all_70_3) = % 23.95/3.99 | all_82_0 & remove_cpq(all_82_0, all_70_0) = all_82_1 & $i(all_82_0) & % 23.95/3.99 | $i(all_82_1) % 23.95/3.99 | % 23.95/3.99 | ALPHA: (39) implies: % 23.95/3.99 | (40) findmin_cpq_eff(all_70_3) = all_82_0 % 23.95/3.99 | % 23.95/3.99 | DELTA: instantiating (34) with fresh symbols all_84_0, all_84_1 gives: % 23.95/3.99 | (41) (findmin_cpq_res(all_70_3) = all_84_1 & $i(all_84_1) & % 23.95/3.99 | contains_cpq(all_70_3, all_84_1)) | (findmin_cpq_eff(all_70_3) = % 23.95/3.99 | all_84_0 & $i(all_84_0) & ~ ok(all_84_0)) % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (14) with all_70_2, all_82_0, all_70_3, simplifying % 23.95/3.99 | with (24), (40) gives: % 23.95/3.99 | (42) all_82_0 = all_70_2 % 23.95/3.99 | % 23.95/3.99 | GROUND_INST: instantiating (16) with all_70_0, all_80_0, all_70_3, simplifying % 23.95/3.99 | with (26), (38) gives: % 23.95/3.99 | (43) all_80_0 = all_70_0 % 23.95/3.99 | % 23.95/3.99 | BETA: splitting (32) gives: % 23.95/3.99 | % 23.95/3.99 | Case 1: % 23.95/3.99 | | % 23.95/3.99 | | (44) ~ (triple(all_70_6, create_slb, all_70_4) = all_70_3) % 23.95/3.99 | | % 23.95/3.99 | | PRED_UNIFY: (25), (44) imply: % 23.95/3.99 | | (45) ~ (all_70_5 = create_slb) % 23.95/3.99 | | % 23.95/3.99 | | BETA: splitting (35) gives: % 23.95/3.99 | | % 23.95/3.99 | | Case 1: % 23.95/3.99 | | | % 23.95/3.99 | | | (46) all_70_5 = create_slb % 23.95/3.99 | | | % 23.95/3.99 | | | REDUCE: (45), (46) imply: % 23.95/4.00 | | | (47) $false % 23.95/4.00 | | | % 23.95/4.00 | | | CLOSE: (47) is inconsistent. % 23.95/4.00 | | | % 23.95/4.00 | | Case 2: % 23.95/4.00 | | | % 23.95/4.00 | | | (48) findmin_pqp_res(all_70_6) = all_70_0 & $i(all_70_0) % 23.95/4.00 | | | % 23.95/4.00 | | | ALPHA: (48) implies: % 23.95/4.00 | | | (49) findmin_pqp_res(all_70_6) = all_70_0 % 23.95/4.00 | | | % 23.95/4.00 | | | BETA: splitting (31) gives: % 23.95/4.00 | | | % 23.95/4.00 | | | Case 1: % 23.95/4.00 | | | | % 23.95/4.00 | | | | (50) all_70_5 = create_slb % 23.95/4.00 | | | | % 23.95/4.00 | | | | REDUCE: (45), (50) imply: % 23.95/4.00 | | | | (51) $false % 23.95/4.00 | | | | % 23.95/4.00 | | | | CLOSE: (51) is inconsistent. % 23.95/4.00 | | | | % 23.95/4.00 | | | Case 2: % 23.95/4.00 | | | | % 23.95/4.00 | | | | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : % 23.95/4.00 | | | | (findmin_pqp_res(all_70_6) = v0 & $i(v0) & % 23.95/4.00 | | | | (contains_slb(all_70_5, v0) | (v2 = all_70_2 & % 23.95/4.00 | | | | triple(all_70_6, v1, bad) = all_70_2 & % 23.95/4.00 | | | | update_slb(all_70_5, v0) = v1 & $i(v1) & $i(all_70_2)))) % 23.95/4.00 | | | | % 23.95/4.00 | | | | DELTA: instantiating (52) with fresh symbols all_162_0, all_162_1, % 23.95/4.00 | | | | all_162_2 gives: % 23.95/4.00 | | | | (53) findmin_pqp_res(all_70_6) = all_162_2 & $i(all_162_2) & % 23.95/4.00 | | | | (contains_slb(all_70_5, all_162_2) | (all_162_0 = all_70_2 & % 23.95/4.00 | | | | triple(all_70_6, all_162_1, bad) = all_70_2 & % 23.95/4.00 | | | | update_slb(all_70_5, all_162_2) = all_162_1 & $i(all_162_1) % 23.95/4.00 | | | | & $i(all_70_2))) % 23.95/4.00 | | | | % 23.95/4.00 | | | | ALPHA: (53) implies: % 23.95/4.00 | | | | (54) $i(all_162_2) % 23.95/4.00 | | | | (55) findmin_pqp_res(all_70_6) = all_162_2 % 23.95/4.00 | | | | (56) contains_slb(all_70_5, all_162_2) | (all_162_0 = all_70_2 & % 23.95/4.00 | | | | triple(all_70_6, all_162_1, bad) = all_70_2 & % 23.95/4.00 | | | | update_slb(all_70_5, all_162_2) = all_162_1 & $i(all_162_1) & % 23.95/4.00 | | | | $i(all_70_2)) % 23.95/4.00 | | | | % 23.95/4.00 | | | | BETA: splitting (30) gives: % 23.95/4.00 | | | | % 23.95/4.00 | | | | Case 1: % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | (57) all_70_5 = create_slb % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | REDUCE: (45), (57) imply: % 23.95/4.00 | | | | | (58) $false % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | CLOSE: (58) is inconsistent. % 23.95/4.00 | | | | | % 23.95/4.00 | | | | Case 2: % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 23.95/4.00 | | | | | (findmin_pqp_res(all_70_6) = v0 & $i(v0) & ( ~ % 23.95/4.00 | | | | | contains_slb(all_70_5, v0) | (v3 = all_70_2 & % 23.95/4.00 | | | | | triple(all_70_6, v2, bad) = all_70_2 & % 23.95/4.00 | | | | | update_slb(all_70_5, v0) = v2 & $i(v2) & $i(all_70_2)) | % 23.95/4.00 | | | | | (lookup_slb(all_70_5, v0) = v1 & $i(v1) & ~ % 23.95/4.00 | | | | | strictly_less_than(v0, v1)))) % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | DELTA: instantiating (59) with fresh symbols all_168_0, all_168_1, % 23.95/4.00 | | | | | all_168_2, all_168_3 gives: % 23.95/4.00 | | | | | (60) findmin_pqp_res(all_70_6) = all_168_3 & $i(all_168_3) & ( ~ % 23.95/4.00 | | | | | contains_slb(all_70_5, all_168_3) | (all_168_0 = all_70_2 & % 23.95/4.00 | | | | | triple(all_70_6, all_168_1, bad) = all_70_2 & % 23.95/4.00 | | | | | update_slb(all_70_5, all_168_3) = all_168_1 & % 23.95/4.00 | | | | | $i(all_168_1) & $i(all_70_2)) | (lookup_slb(all_70_5, % 23.95/4.00 | | | | | all_168_3) = all_168_2 & $i(all_168_2) & ~ % 23.95/4.00 | | | | | strictly_less_than(all_168_3, all_168_2))) % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | ALPHA: (60) implies: % 23.95/4.00 | | | | | (61) findmin_pqp_res(all_70_6) = all_168_3 % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | BETA: splitting (29) gives: % 23.95/4.00 | | | | | % 23.95/4.00 | | | | | Case 1: % 23.95/4.00 | | | | | | % 23.95/4.00 | | | | | | (62) all_70_5 = create_slb % 23.95/4.00 | | | | | | % 23.95/4.00 | | | | | | REDUCE: (45), (62) imply: % 23.95/4.00 | | | | | | (63) $false % 23.95/4.00 | | | | | | % 23.95/4.00 | | | | | | CLOSE: (63) is inconsistent. % 23.95/4.00 | | | | | | % 23.95/4.00 | | | | | Case 2: % 23.95/4.00 | | | | | | % 23.95/4.00 | | | | | | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : % 23.95/4.00 | | | | | | (findmin_pqp_res(all_70_6) = v0 & $i(v0) & ( ~ % 23.95/4.00 | | | | | | contains_slb(all_70_5, v0) | (v3 = all_70_2 & % 23.95/4.00 | | | | | | triple(all_70_6, v2, all_70_4) = all_70_2 & % 23.95/4.00 | | | | | | update_slb(all_70_5, v0) = v2 & $i(v2) & $i(all_70_2)) % 23.95/4.00 | | | | | | | (lookup_slb(all_70_5, v0) = v1 & $i(v1) & ~ % 23.95/4.00 | | | | | | less_than(v1, v0)))) % 23.95/4.00 | | | | | | % 23.95/4.00 | | | | | | DELTA: instantiating (64) with fresh symbols all_173_0, all_173_1, % 23.95/4.00 | | | | | | all_173_2, all_173_3 gives: % 23.95/4.00 | | | | | | (65) findmin_pqp_res(all_70_6) = all_173_3 & $i(all_173_3) & ( ~ % 23.95/4.00 | | | | | | contains_slb(all_70_5, all_173_3) | (all_173_0 = all_70_2 % 23.95/4.00 | | | | | | & triple(all_70_6, all_173_1, all_70_4) = all_70_2 & % 23.95/4.00 | | | | | | update_slb(all_70_5, all_173_3) = all_173_1 & % 23.95/4.00 | | | | | | $i(all_173_1) & $i(all_70_2)) | (lookup_slb(all_70_5, % 23.95/4.00 | | | | | | all_173_3) = all_173_2 & $i(all_173_2) & ~ % 23.95/4.00 | | | | | | less_than(all_173_2, all_173_3))) % 23.95/4.00 | | | | | | % 23.95/4.00 | | | | | | ALPHA: (65) implies: % 23.95/4.00 | | | | | | (66) findmin_pqp_res(all_70_6) = all_173_3 % 23.95/4.00 | | | | | | (67) ~ contains_slb(all_70_5, all_173_3) | (all_173_0 = all_70_2 % 23.95/4.00 | | | | | | & triple(all_70_6, all_173_1, all_70_4) = all_70_2 & % 23.95/4.00 | | | | | | update_slb(all_70_5, all_173_3) = all_173_1 & % 23.95/4.00 | | | | | | $i(all_173_1) & $i(all_70_2)) | (lookup_slb(all_70_5, % 23.95/4.00 | | | | | | all_173_3) = all_173_2 & $i(all_173_2) & ~ % 23.95/4.00 | | | | | | less_than(all_173_2, all_173_3)) % 23.95/4.00 | | | | | | % 23.95/4.01 | | | | | | GROUND_INST: instantiating (15) with all_162_2, all_168_3, all_70_6, % 23.95/4.01 | | | | | | simplifying with (55), (61) gives: % 23.95/4.01 | | | | | | (68) all_168_3 = all_162_2 % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | GROUND_INST: instantiating (15) with all_168_3, all_173_3, all_70_6, % 23.95/4.01 | | | | | | simplifying with (61), (66) gives: % 23.95/4.01 | | | | | | (69) all_173_3 = all_168_3 % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | GROUND_INST: instantiating (15) with all_70_0, all_173_3, all_70_6, % 23.95/4.01 | | | | | | simplifying with (49), (66) gives: % 23.95/4.01 | | | | | | (70) all_173_3 = all_70_0 % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | COMBINE_EQS: (69), (70) imply: % 23.95/4.01 | | | | | | (71) all_168_3 = all_70_0 % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | SIMP: (71) implies: % 23.95/4.01 | | | | | | (72) all_168_3 = all_70_0 % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | COMBINE_EQS: (68), (72) imply: % 23.95/4.01 | | | | | | (73) all_162_2 = all_70_0 % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | REDUCE: (54), (73) imply: % 23.95/4.01 | | | | | | (74) $i(all_70_0) % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | BETA: splitting (41) gives: % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | | Case 1: % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | (75) findmin_cpq_res(all_70_3) = all_84_1 & $i(all_84_1) & % 23.95/4.01 | | | | | | | contains_cpq(all_70_3, all_84_1) % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | ALPHA: (75) implies: % 23.95/4.01 | | | | | | | (76) contains_cpq(all_70_3, all_84_1) % 23.95/4.01 | | | | | | | (77) $i(all_84_1) % 23.95/4.01 | | | | | | | (78) findmin_cpq_res(all_70_3) = all_84_1 % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | GROUND_INST: instantiating (16) with all_70_0, all_84_1, all_70_3, % 23.95/4.01 | | | | | | | simplifying with (26), (78) gives: % 23.95/4.01 | | | | | | | (79) all_84_1 = all_70_0 % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | REDUCE: (76), (79) imply: % 23.95/4.01 | | | | | | | (80) contains_cpq(all_70_3, all_70_0) % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | GROUND_INST: instantiating (13) with all_70_6, all_70_5, all_70_4, % 23.95/4.01 | | | | | | | all_70_0, all_70_3, all_70_1, simplifying with (18), % 23.95/4.01 | | | | | | | (20), (21), (22), (25), (27), (74), (80) gives: % 23.95/4.01 | | | | | | | (81) $false % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | CLOSE: (81) is inconsistent. % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | Case 2: % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | (82) findmin_cpq_eff(all_70_3) = all_84_0 & $i(all_84_0) & ~ % 23.95/4.01 | | | | | | | ok(all_84_0) % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | ALPHA: (82) implies: % 23.95/4.01 | | | | | | | (83) ~ ok(all_84_0) % 23.95/4.01 | | | | | | | (84) findmin_cpq_eff(all_70_3) = all_84_0 % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | GROUND_INST: instantiating (14) with all_70_2, all_84_0, all_70_3, % 23.95/4.01 | | | | | | | simplifying with (24), (84) gives: % 23.95/4.01 | | | | | | | (85) all_84_0 = all_70_2 % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | REDUCE: (83), (85) imply: % 23.95/4.01 | | | | | | | (86) ~ ok(all_70_2) % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | BETA: splitting (56) gives: % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | | Case 1: % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | (87) contains_slb(all_70_5, all_162_2) % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | REDUCE: (73), (87) imply: % 23.95/4.01 | | | | | | | | (88) contains_slb(all_70_5, all_70_0) % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | BETA: splitting (67) gives: % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | Case 1: % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | (89) ~ contains_slb(all_70_5, all_173_3) % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | REDUCE: (70), (89) imply: % 23.95/4.01 | | | | | | | | | (90) ~ contains_slb(all_70_5, all_70_0) % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | PRED_UNIFY: (88), (90) imply: % 23.95/4.01 | | | | | | | | | (91) $false % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | CLOSE: (91) is inconsistent. % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | Case 2: % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | (92) contains_slb(all_70_5, all_173_3) % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | GROUND_INST: instantiating (2) with all_70_6, all_70_5, % 23.95/4.01 | | | | | | | | | all_70_4, all_70_0, all_70_3, simplifying with % 23.95/4.01 | | | | | | | | | (20), (21), (22), (25), (74), (88) gives: % 23.95/4.01 | | | | | | | | | (93) contains_cpq(all_70_3, all_70_0) % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | GROUND_INST: instantiating (13) with all_70_6, all_70_5, % 23.95/4.01 | | | | | | | | | all_70_4, all_70_0, all_70_3, all_70_1, % 23.95/4.01 | | | | | | | | | simplifying with (18), (20), (21), (22), (25), % 23.95/4.01 | | | | | | | | | (27), (74), (93) gives: % 23.95/4.01 | | | | | | | | | (94) $false % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | | CLOSE: (94) is inconsistent. % 23.95/4.01 | | | | | | | | | % 23.95/4.01 | | | | | | | | End of split % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | Case 2: % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | (95) all_162_0 = all_70_2 & triple(all_70_6, all_162_1, bad) % 23.95/4.01 | | | | | | | | = all_70_2 & update_slb(all_70_5, all_162_2) = all_162_1 % 23.95/4.01 | | | | | | | | & $i(all_162_1) & $i(all_70_2) % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | ALPHA: (95) implies: % 23.95/4.01 | | | | | | | | (96) $i(all_162_1) % 23.95/4.01 | | | | | | | | (97) triple(all_70_6, all_162_1, bad) = all_70_2 % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | GROUND_INST: instantiating (l8_lX) with all_70_6, all_162_1, % 23.95/4.01 | | | | | | | | bad, all_70_2, simplifying with (6), (19), (20), % 23.95/4.01 | | | | | | | | (86), (96), (97) gives: % 23.95/4.01 | | | | | | | | (98) $false % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | | CLOSE: (98) is inconsistent. % 23.95/4.01 | | | | | | | | % 23.95/4.01 | | | | | | | End of split % 23.95/4.01 | | | | | | | % 23.95/4.01 | | | | | | End of split % 23.95/4.01 | | | | | | % 23.95/4.01 | | | | | End of split % 23.95/4.01 | | | | | % 23.95/4.01 | | | | End of split % 23.95/4.01 | | | | % 23.95/4.01 | | | End of split % 23.95/4.01 | | | % 23.95/4.01 | | End of split % 23.95/4.01 | | % 23.95/4.01 | Case 2: % 23.95/4.01 | | % 23.95/4.01 | | (99) triple(all_70_6, create_slb, all_70_4) = all_70_3 % 23.95/4.01 | | % 23.95/4.01 | | BETA: splitting (33) gives: % 23.95/4.01 | | % 23.95/4.01 | | Case 1: % 23.95/4.01 | | | % 23.95/4.01 | | | (100) ~ (triple(all_70_6, create_slb, all_70_4) = all_70_3) % 23.95/4.01 | | | % 23.95/4.01 | | | PRED_UNIFY: (99), (100) imply: % 23.95/4.01 | | | (101) $false % 23.95/4.01 | | | % 23.95/4.01 | | | CLOSE: (101) is inconsistent. % 23.95/4.01 | | | % 23.95/4.01 | | Case 2: % 23.95/4.01 | | | % 23.95/4.02 | | | (102) ? [v0: $i] : (triple(all_70_6, create_slb, bad) = v0 & % 23.95/4.02 | | | findmin_cpq_eff(all_70_3) = v0 & $i(v0)) % 23.95/4.02 | | | % 23.95/4.02 | | | DELTA: instantiating (102) with fresh symbol all_155_0 gives: % 23.95/4.02 | | | (103) triple(all_70_6, create_slb, bad) = all_155_0 & % 23.95/4.02 | | | findmin_cpq_eff(all_70_3) = all_155_0 & $i(all_155_0) % 23.95/4.02 | | | % 23.95/4.02 | | | ALPHA: (103) implies: % 23.95/4.02 | | | (104) findmin_cpq_eff(all_70_3) = all_155_0 % 23.95/4.02 | | | (105) triple(all_70_6, create_slb, bad) = all_155_0 % 23.95/4.02 | | | % 23.95/4.02 | | | GROUND_INST: instantiating (14) with all_70_2, all_155_0, all_70_3, % 23.95/4.02 | | | simplifying with (24), (104) gives: % 23.95/4.02 | | | (106) all_155_0 = all_70_2 % 23.95/4.02 | | | % 23.95/4.02 | | | REDUCE: (105), (106) imply: % 23.95/4.02 | | | (107) triple(all_70_6, create_slb, bad) = all_70_2 % 23.95/4.02 | | | % 23.95/4.02 | | | GROUND_INST: instantiating (l8_lX) with all_70_6, create_slb, bad, % 23.95/4.02 | | | all_70_2, simplifying with (6), (12), (19), (20), (107) % 23.95/4.02 | | | gives: % 23.95/4.02 | | | (108) ok(all_70_2) % 23.95/4.02 | | | % 23.95/4.02 | | | GROUND_INST: instantiating (3) with all_70_6, create_slb, all_70_2, % 23.95/4.02 | | | simplifying with (12), (20), (107) gives: % 23.95/4.02 | | | (109) ~ ok(all_70_2) % 23.95/4.02 | | | % 23.95/4.02 | | | PRED_UNIFY: (108), (109) imply: % 23.95/4.02 | | | (110) $false % 23.95/4.02 | | | % 23.95/4.02 | | | CLOSE: (110) is inconsistent. % 23.95/4.02 | | | % 23.95/4.02 | | End of split % 23.95/4.02 | | % 23.95/4.02 | End of split % 23.95/4.02 | % 23.95/4.02 End of proof % 23.95/4.02 % SZS output end Proof for theBenchmark % 23.95/4.02 % 23.95/4.02 3429ms %------------------------------------------------------------------------------